CNN -Tropical Storm Isaac, currently moving through the Caribbean south of Puerto Rico, is on a path that could lead it to vulnerable Haiti at hurricane strength Friday night.

A hurricane warning is already in place for all of Haiti, a country that is still recovering from a devastating 2010 earthquake. As many of 12 inches of rain are forecast for some parts of the country, posing danger to the more than 400,000 Haitians who live in camps.

Isaac also poses a risk it poses to the Republican National Convention in Florida. The storm could hit anywhere in Florida, Gov. Rick Scott said Thursday, and it will be up to convention organizers to decide the fate of the event.

But before it nears Florida, Isaac is forecast to run over Hispaniola, the island where Haiti and the Dominican Republic are located.

As of 8 a.m. ET, Isaac was about 225 miles (360 kilometers) south-southeast of San Juan, Puerto Rico, the center said.

It was moving to the west near 13 mph with maximum sustained winds near 40 mph.

The center of the storm is forecast to pass to the south of the Virgin Islands and Puerto Rico on Thursday, and approach the Dominican Republic Thursday night and into Friday, the center said.

While the storm is yet to reach hurricane strength, it has already delivered shock waves from the Caribbean to Florida, postponing terror trials at the U.S. naval base in Guantanamo Bay, Cuba, and.

"Re-strengthening is forecast during the next 48 hours, and Isaac could still become a hurricane on Friday before it reaches Hispaniola," according to forecasters.

Aid organizations were keeping an eye on Haiti, where hundreds of thousands still live in camps after the deadly earthquake.

According to the U.N. High Commissioner for Refugees, 421,000 people are in camps in and around Port-au-Prince.

Isaac could be the first significant storm to hit Haiti since the devastating earthquake. Tropical Storm Emily threatened in 2011, but it weakened before hitting western Haiti.

The forecast map shows Isaac crossing the nation as a tropical storm with winds under 74 mph.

"We watch those storms every single time they come near because Haiti is so vulnerable," said Amy Parodi, a spokeswoman for the Christian humanitarian organization World Vision.

The agency has met with the government in previous summers to discuss contingency plans for major storms, and pre-positioned relief items are available, she said.

Isaac's path remains uncertain, but some computer models show the storm slicing its way up Florida's peninsula. Others send it farther west, into the Gulf of Mexico.

Officials are taking the threat seriously.

"Obviously, we hope Isaac doesn't hit Florida, but we must take every precaution," Scott said.

While the convention will have the final say on any changes to the planned event, the organizers are working together with state and local officials to ensure everyone has the same information, the governor said.

But Tampa is not the only part of Florida that could potentially be hit, and Scott urged Floridians to be prepared.

"What everyone needs to do is to starting tracking it, watch the weather, heed any warnings, get ready, get 72 hours worth of supplies," he said.

Tampa Mayor Bob Buckhorn said his city is prepared for the 50,000 people headed to his city for the Republican National Convention, which starts Monday.

"We have contingency plan after contingency plan," Buckhorn said. "We are ready in the event that it happens. I don't think it's going to be a factor in this particular convention. But we are prepared in the event that it is."

Convention spokesman Kyle Downey said the situation is being monitored "very closely."

Possibly complicating matters, the convention site -- The Tampa Bay Times Forum -- is a mandatory evacuation zone once storms reach 96 mph, a Category 2 hurricane, according to the Hillsborough County Hurricane Guide. The current forecast doesn't have Isaac reaching that status.

At the U.S. naval base at Guantanamo Bay, officials canceled the pretrial arguments scheduled to get under way in the trial of Khalid Sheikh Mohammed and four others.

Mohammed -- who has been held since 2006 -- is facing charges related to the September 11, 2001, terrorist attacks.

Pentagon officials said all court events at Guantanamo were canceled because of the potential hurricane. All detainees have been moved to buildings that can withstand such a storm, and those who flew in for the hearing went back home.

Officials in the Dominican Republic issued a hurricane warning along the nation's southern coast. The nation's center of emergency operations put 18 provinces under red alert as the storm advances.

Tropical storm warnings covered much of the Leeward Islands, as well as Puerto Rico and the Virgin Islands.

Isaac could bring 4 to 8 inches of rain over the Northern Windward Islands and the Leeward Islands, the center said, and up to 6 inches of rain in Puerto Rico and the Virgin Islands.

On Hispaniola, 8 to 12 inches of rain, with maximum amounts of 20 inches, are possible, the center said.

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